An artihmetic series has first term \(a\) and common difference \(4369a\), where \(a\ne 0\). A geometric series has first term \(a\) and common ratio \(2\). The \(\left( n+1 \right)\)th term of the geometric series is equal to the \(n\)th term of the arithmetic series, where \(n>1\). Find the value of \(n\).[4]
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